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Some Six-Dimensional Rigid Forms


Dutour, Mathieu; Vallentin, Frank
Some Six-Dimensional Rigid Forms // Voronoi's Impact on Modern Science, Book 3, Vol.55 of Proc. Inst. Math. Nat. Acad. Sci. / Syta, H. ; Yurachivsky, A. ; Engel, P. (ur.).
Kiev: National academy of science of Ukraine, 2005. str. 102-108


Naslov
Some Six-Dimensional Rigid Forms

Autori
Dutour, Mathieu ; Vallentin, Frank

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Voronoi's Impact on Modern Science, Book 3, Vol.55 of Proc. Inst. Math. Nat. Acad. Sci.

Urednik/ci
Syta, H. ; Yurachivsky, A. ; Engel, P.

Izdavač
National academy of science of Ukraine

Grad
Kiev

Godina
2005

Raspon stranica
102-108

ISBN
966-02-2571-7

Ključne riječi
dual description, rigid forms, L-type

Sažetak
One can always decompose Dirichlet-Voronoi polytopes of lattices non-trivially into a Minkowski sum of Dirichlet-Voronoi polytopes of rigid lattices. In this report we show how one can enumerate all rigid positive semidefinite quadratic forms (and thereby rigid lattices) of a given dimension d. By this method we found all rigid positive semidefinite quadratic forms for d=5 confirming the list of 7 rigid lattices by Baranovskii and Grishukhin. Furthermore, we found out that for d<=5 the adjacency graph of primitive L-type domains is an infinite tree on which GLd(Z) acts. On the other hand, we demonstrate that in d=6 we face a combinatorial explosion.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Ustanove
Institut "Ruđer Bošković", Zagreb

Profili:

Avatar Url Mathieu Dutour Sikirić (autor)

Citiraj ovu publikaciju

Dutour, Mathieu; Vallentin, Frank
Some Six-Dimensional Rigid Forms // Voronoi's Impact on Modern Science, Book 3, Vol.55 of Proc. Inst. Math. Nat. Acad. Sci. / Syta, H. ; Yurachivsky, A. ; Engel, P. (ur.).
Kiev: National academy of science of Ukraine, 2005. str. 102-108
Dutour, M. & Vallentin, F. (2005) Some Six-Dimensional Rigid Forms. U: Syta, H., Yurachivsky, A. & Engel, P. (ur.) Voronoi's Impact on Modern Science, Book 3, Vol.55 of Proc. Inst. Math. Nat. Acad. Sci.. Kiev, National academy of science of Ukraine, str. 102-108.
@inbook{inbook, year = {2005}, pages = {102-108}, keywords = {dual description, rigid forms, L-type}, isbn = {966-02-2571-7}, title = {Some Six-Dimensional Rigid Forms}, keyword = {dual description, rigid forms, L-type}, publisher = {National academy of science of Ukraine}, publisherplace = {Kiev} }